Properties

Label 8035.2.a.e.1.14
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.41769 q^{2}\) \(-0.844619 q^{3}\) \(+3.84521 q^{4}\) \(+1.00000 q^{5}\) \(+2.04202 q^{6}\) \(+0.104455 q^{7}\) \(-4.46113 q^{8}\) \(-2.28662 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.41769 q^{2}\) \(-0.844619 q^{3}\) \(+3.84521 q^{4}\) \(+1.00000 q^{5}\) \(+2.04202 q^{6}\) \(+0.104455 q^{7}\) \(-4.46113 q^{8}\) \(-2.28662 q^{9}\) \(-2.41769 q^{10}\) \(-4.33837 q^{11}\) \(-3.24773 q^{12}\) \(+1.66281 q^{13}\) \(-0.252539 q^{14}\) \(-0.844619 q^{15}\) \(+3.09520 q^{16}\) \(-2.04843 q^{17}\) \(+5.52833 q^{18}\) \(-3.17857 q^{19}\) \(+3.84521 q^{20}\) \(-0.0882245 q^{21}\) \(+10.4888 q^{22}\) \(-3.39580 q^{23}\) \(+3.76795 q^{24}\) \(+1.00000 q^{25}\) \(-4.02016 q^{26}\) \(+4.46518 q^{27}\) \(+0.401650 q^{28}\) \(+3.48617 q^{29}\) \(+2.04202 q^{30}\) \(+1.88643 q^{31}\) \(+1.43905 q^{32}\) \(+3.66427 q^{33}\) \(+4.95246 q^{34}\) \(+0.104455 q^{35}\) \(-8.79252 q^{36}\) \(-2.54978 q^{37}\) \(+7.68478 q^{38}\) \(-1.40444 q^{39}\) \(-4.46113 q^{40}\) \(+1.81376 q^{41}\) \(+0.213299 q^{42}\) \(-6.32258 q^{43}\) \(-16.6819 q^{44}\) \(-2.28662 q^{45}\) \(+8.20998 q^{46}\) \(+10.7097 q^{47}\) \(-2.61426 q^{48}\) \(-6.98909 q^{49}\) \(-2.41769 q^{50}\) \(+1.73014 q^{51}\) \(+6.39386 q^{52}\) \(-11.1272 q^{53}\) \(-10.7954 q^{54}\) \(-4.33837 q^{55}\) \(-0.465986 q^{56}\) \(+2.68468 q^{57}\) \(-8.42845 q^{58}\) \(+13.0910 q^{59}\) \(-3.24773 q^{60}\) \(-8.38124 q^{61}\) \(-4.56079 q^{62}\) \(-0.238848 q^{63}\) \(-9.66955 q^{64}\) \(+1.66281 q^{65}\) \(-8.85906 q^{66}\) \(-13.6304 q^{67}\) \(-7.87663 q^{68}\) \(+2.86816 q^{69}\) \(-0.252539 q^{70}\) \(-0.521308 q^{71}\) \(+10.2009 q^{72}\) \(-4.01401 q^{73}\) \(+6.16457 q^{74}\) \(-0.844619 q^{75}\) \(-12.2223 q^{76}\) \(-0.453164 q^{77}\) \(+3.39551 q^{78}\) \(+12.4879 q^{79}\) \(+3.09520 q^{80}\) \(+3.08848 q^{81}\) \(-4.38511 q^{82}\) \(-2.23895 q^{83}\) \(-0.339241 q^{84}\) \(-2.04843 q^{85}\) \(+15.2860 q^{86}\) \(-2.94448 q^{87}\) \(+19.3540 q^{88}\) \(-15.5780 q^{89}\) \(+5.52833 q^{90}\) \(+0.173689 q^{91}\) \(-13.0575 q^{92}\) \(-1.59331 q^{93}\) \(-25.8927 q^{94}\) \(-3.17857 q^{95}\) \(-1.21545 q^{96}\) \(-16.2681 q^{97}\) \(+16.8974 q^{98}\) \(+9.92020 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41769 −1.70956 −0.854781 0.518989i \(-0.826309\pi\)
−0.854781 + 0.518989i \(0.826309\pi\)
\(3\) −0.844619 −0.487641 −0.243821 0.969820i \(-0.578401\pi\)
−0.243821 + 0.969820i \(0.578401\pi\)
\(4\) 3.84521 1.92260
\(5\) 1.00000 0.447214
\(6\) 2.04202 0.833653
\(7\) 0.104455 0.0394802 0.0197401 0.999805i \(-0.493716\pi\)
0.0197401 + 0.999805i \(0.493716\pi\)
\(8\) −4.46113 −1.57725
\(9\) −2.28662 −0.762206
\(10\) −2.41769 −0.764539
\(11\) −4.33837 −1.30807 −0.654034 0.756465i \(-0.726925\pi\)
−0.654034 + 0.756465i \(0.726925\pi\)
\(12\) −3.24773 −0.937540
\(13\) 1.66281 0.461182 0.230591 0.973051i \(-0.425934\pi\)
0.230591 + 0.973051i \(0.425934\pi\)
\(14\) −0.252539 −0.0674938
\(15\) −0.844619 −0.218080
\(16\) 3.09520 0.773799
\(17\) −2.04843 −0.496817 −0.248409 0.968655i \(-0.579908\pi\)
−0.248409 + 0.968655i \(0.579908\pi\)
\(18\) 5.52833 1.30304
\(19\) −3.17857 −0.729214 −0.364607 0.931162i \(-0.618797\pi\)
−0.364607 + 0.931162i \(0.618797\pi\)
\(20\) 3.84521 0.859814
\(21\) −0.0882245 −0.0192522
\(22\) 10.4888 2.23622
\(23\) −3.39580 −0.708073 −0.354037 0.935232i \(-0.615191\pi\)
−0.354037 + 0.935232i \(0.615191\pi\)
\(24\) 3.76795 0.769130
\(25\) 1.00000 0.200000
\(26\) −4.02016 −0.788419
\(27\) 4.46518 0.859324
\(28\) 0.401650 0.0759047
\(29\) 3.48617 0.647365 0.323682 0.946166i \(-0.395079\pi\)
0.323682 + 0.946166i \(0.395079\pi\)
\(30\) 2.04202 0.372821
\(31\) 1.88643 0.338812 0.169406 0.985546i \(-0.445815\pi\)
0.169406 + 0.985546i \(0.445815\pi\)
\(32\) 1.43905 0.254390
\(33\) 3.66427 0.637868
\(34\) 4.95246 0.849340
\(35\) 0.104455 0.0176561
\(36\) −8.79252 −1.46542
\(37\) −2.54978 −0.419182 −0.209591 0.977789i \(-0.567213\pi\)
−0.209591 + 0.977789i \(0.567213\pi\)
\(38\) 7.68478 1.24664
\(39\) −1.40444 −0.224891
\(40\) −4.46113 −0.705366
\(41\) 1.81376 0.283262 0.141631 0.989920i \(-0.454765\pi\)
0.141631 + 0.989920i \(0.454765\pi\)
\(42\) 0.213299 0.0329128
\(43\) −6.32258 −0.964184 −0.482092 0.876121i \(-0.660123\pi\)
−0.482092 + 0.876121i \(0.660123\pi\)
\(44\) −16.6819 −2.51490
\(45\) −2.28662 −0.340869
\(46\) 8.20998 1.21050
\(47\) 10.7097 1.56217 0.781085 0.624425i \(-0.214666\pi\)
0.781085 + 0.624425i \(0.214666\pi\)
\(48\) −2.61426 −0.377336
\(49\) −6.98909 −0.998441
\(50\) −2.41769 −0.341912
\(51\) 1.73014 0.242268
\(52\) 6.39386 0.886669
\(53\) −11.1272 −1.52844 −0.764220 0.644956i \(-0.776876\pi\)
−0.764220 + 0.644956i \(0.776876\pi\)
\(54\) −10.7954 −1.46907
\(55\) −4.33837 −0.584986
\(56\) −0.465986 −0.0622700
\(57\) 2.68468 0.355595
\(58\) −8.42845 −1.10671
\(59\) 13.0910 1.70430 0.852149 0.523299i \(-0.175299\pi\)
0.852149 + 0.523299i \(0.175299\pi\)
\(60\) −3.24773 −0.419281
\(61\) −8.38124 −1.07311 −0.536554 0.843866i \(-0.680274\pi\)
−0.536554 + 0.843866i \(0.680274\pi\)
\(62\) −4.56079 −0.579220
\(63\) −0.238848 −0.0300920
\(64\) −9.66955 −1.20869
\(65\) 1.66281 0.206247
\(66\) −8.85906 −1.09047
\(67\) −13.6304 −1.66522 −0.832609 0.553861i \(-0.813154\pi\)
−0.832609 + 0.553861i \(0.813154\pi\)
\(68\) −7.87663 −0.955182
\(69\) 2.86816 0.345286
\(70\) −0.252539 −0.0301842
\(71\) −0.521308 −0.0618678 −0.0309339 0.999521i \(-0.509848\pi\)
−0.0309339 + 0.999521i \(0.509848\pi\)
\(72\) 10.2009 1.20219
\(73\) −4.01401 −0.469805 −0.234902 0.972019i \(-0.575477\pi\)
−0.234902 + 0.972019i \(0.575477\pi\)
\(74\) 6.16457 0.716617
\(75\) −0.844619 −0.0975282
\(76\) −12.2223 −1.40199
\(77\) −0.453164 −0.0516428
\(78\) 3.39551 0.384465
\(79\) 12.4879 1.40499 0.702497 0.711687i \(-0.252068\pi\)
0.702497 + 0.711687i \(0.252068\pi\)
\(80\) 3.09520 0.346053
\(81\) 3.08848 0.343164
\(82\) −4.38511 −0.484254
\(83\) −2.23895 −0.245756 −0.122878 0.992422i \(-0.539212\pi\)
−0.122878 + 0.992422i \(0.539212\pi\)
\(84\) −0.339241 −0.0370143
\(85\) −2.04843 −0.222183
\(86\) 15.2860 1.64833
\(87\) −2.94448 −0.315682
\(88\) 19.3540 2.06315
\(89\) −15.5780 −1.65127 −0.825634 0.564206i \(-0.809182\pi\)
−0.825634 + 0.564206i \(0.809182\pi\)
\(90\) 5.52833 0.582737
\(91\) 0.173689 0.0182075
\(92\) −13.0575 −1.36134
\(93\) −1.59331 −0.165219
\(94\) −25.8927 −2.67063
\(95\) −3.17857 −0.326114
\(96\) −1.21545 −0.124051
\(97\) −16.2681 −1.65178 −0.825889 0.563832i \(-0.809326\pi\)
−0.825889 + 0.563832i \(0.809326\pi\)
\(98\) 16.8974 1.70690
\(99\) 9.92020 0.997018
\(100\) 3.84521 0.384521
\(101\) −7.87060 −0.783154 −0.391577 0.920145i \(-0.628070\pi\)
−0.391577 + 0.920145i \(0.628070\pi\)
\(102\) −4.18294 −0.414173
\(103\) −10.2337 −1.00836 −0.504180 0.863599i \(-0.668205\pi\)
−0.504180 + 0.863599i \(0.668205\pi\)
\(104\) −7.41803 −0.727397
\(105\) −0.0882245 −0.00860983
\(106\) 26.9021 2.61296
\(107\) 1.53276 0.148178 0.0740889 0.997252i \(-0.476395\pi\)
0.0740889 + 0.997252i \(0.476395\pi\)
\(108\) 17.1695 1.65214
\(109\) 13.3391 1.27765 0.638825 0.769352i \(-0.279421\pi\)
0.638825 + 0.769352i \(0.279421\pi\)
\(110\) 10.4888 1.00007
\(111\) 2.15359 0.204410
\(112\) 0.323308 0.0305497
\(113\) 13.0921 1.23160 0.615800 0.787902i \(-0.288833\pi\)
0.615800 + 0.787902i \(0.288833\pi\)
\(114\) −6.49071 −0.607911
\(115\) −3.39580 −0.316660
\(116\) 13.4050 1.24463
\(117\) −3.80222 −0.351515
\(118\) −31.6498 −2.91360
\(119\) −0.213968 −0.0196144
\(120\) 3.76795 0.343966
\(121\) 7.82147 0.711043
\(122\) 20.2632 1.83455
\(123\) −1.53194 −0.138130
\(124\) 7.25370 0.651401
\(125\) 1.00000 0.0894427
\(126\) 0.577460 0.0514442
\(127\) −19.9805 −1.77298 −0.886491 0.462746i \(-0.846864\pi\)
−0.886491 + 0.462746i \(0.846864\pi\)
\(128\) 20.4998 1.81195
\(129\) 5.34017 0.470176
\(130\) −4.02016 −0.352592
\(131\) 16.4794 1.43981 0.719905 0.694072i \(-0.244185\pi\)
0.719905 + 0.694072i \(0.244185\pi\)
\(132\) 14.0899 1.22637
\(133\) −0.332017 −0.0287895
\(134\) 32.9540 2.84679
\(135\) 4.46518 0.384301
\(136\) 9.13831 0.783603
\(137\) 12.5847 1.07518 0.537590 0.843206i \(-0.319335\pi\)
0.537590 + 0.843206i \(0.319335\pi\)
\(138\) −6.93430 −0.590287
\(139\) −14.8147 −1.25657 −0.628283 0.777985i \(-0.716242\pi\)
−0.628283 + 0.777985i \(0.716242\pi\)
\(140\) 0.401650 0.0339456
\(141\) −9.04562 −0.761778
\(142\) 1.26036 0.105767
\(143\) −7.21391 −0.603257
\(144\) −7.07753 −0.589794
\(145\) 3.48617 0.289510
\(146\) 9.70462 0.803160
\(147\) 5.90312 0.486881
\(148\) −9.80444 −0.805920
\(149\) 11.6967 0.958230 0.479115 0.877752i \(-0.340958\pi\)
0.479115 + 0.877752i \(0.340958\pi\)
\(150\) 2.04202 0.166731
\(151\) −3.33737 −0.271591 −0.135796 0.990737i \(-0.543359\pi\)
−0.135796 + 0.990737i \(0.543359\pi\)
\(152\) 14.1800 1.15015
\(153\) 4.68398 0.378677
\(154\) 1.09561 0.0882866
\(155\) 1.88643 0.151521
\(156\) −5.40038 −0.432376
\(157\) −3.39499 −0.270950 −0.135475 0.990781i \(-0.543256\pi\)
−0.135475 + 0.990781i \(0.543256\pi\)
\(158\) −30.1917 −2.40193
\(159\) 9.39825 0.745330
\(160\) 1.43905 0.113767
\(161\) −0.354707 −0.0279549
\(162\) −7.46697 −0.586661
\(163\) 4.41601 0.345889 0.172944 0.984932i \(-0.444672\pi\)
0.172944 + 0.984932i \(0.444672\pi\)
\(164\) 6.97429 0.544600
\(165\) 3.66427 0.285263
\(166\) 5.41307 0.420136
\(167\) −11.7157 −0.906589 −0.453295 0.891361i \(-0.649751\pi\)
−0.453295 + 0.891361i \(0.649751\pi\)
\(168\) 0.393581 0.0303654
\(169\) −10.2350 −0.787312
\(170\) 4.95246 0.379836
\(171\) 7.26817 0.555811
\(172\) −24.3116 −1.85374
\(173\) −10.4578 −0.795095 −0.397548 0.917582i \(-0.630139\pi\)
−0.397548 + 0.917582i \(0.630139\pi\)
\(174\) 7.11883 0.539677
\(175\) 0.104455 0.00789604
\(176\) −13.4281 −1.01218
\(177\) −11.0569 −0.831086
\(178\) 37.6628 2.82295
\(179\) 5.05332 0.377703 0.188851 0.982006i \(-0.439524\pi\)
0.188851 + 0.982006i \(0.439524\pi\)
\(180\) −8.79252 −0.655356
\(181\) 12.0260 0.893885 0.446942 0.894563i \(-0.352513\pi\)
0.446942 + 0.894563i \(0.352513\pi\)
\(182\) −0.419925 −0.0311269
\(183\) 7.07896 0.523292
\(184\) 15.1491 1.11681
\(185\) −2.54978 −0.187464
\(186\) 3.85213 0.282452
\(187\) 8.88685 0.649871
\(188\) 41.1810 3.00343
\(189\) 0.466409 0.0339263
\(190\) 7.68478 0.557513
\(191\) 10.2222 0.739653 0.369826 0.929101i \(-0.379417\pi\)
0.369826 + 0.929101i \(0.379417\pi\)
\(192\) 8.16709 0.589409
\(193\) 3.92688 0.282663 0.141332 0.989962i \(-0.454862\pi\)
0.141332 + 0.989962i \(0.454862\pi\)
\(194\) 39.3312 2.82382
\(195\) −1.40444 −0.100574
\(196\) −26.8745 −1.91961
\(197\) −0.838466 −0.0597382 −0.0298691 0.999554i \(-0.509509\pi\)
−0.0298691 + 0.999554i \(0.509509\pi\)
\(198\) −23.9839 −1.70446
\(199\) 22.2877 1.57993 0.789966 0.613151i \(-0.210098\pi\)
0.789966 + 0.613151i \(0.210098\pi\)
\(200\) −4.46113 −0.315449
\(201\) 11.5125 0.812029
\(202\) 19.0286 1.33885
\(203\) 0.364147 0.0255581
\(204\) 6.65276 0.465786
\(205\) 1.81376 0.126679
\(206\) 24.7420 1.72385
\(207\) 7.76490 0.539698
\(208\) 5.14673 0.356862
\(209\) 13.7898 0.953861
\(210\) 0.213299 0.0147190
\(211\) −15.3686 −1.05802 −0.529009 0.848616i \(-0.677436\pi\)
−0.529009 + 0.848616i \(0.677436\pi\)
\(212\) −42.7864 −2.93858
\(213\) 0.440306 0.0301693
\(214\) −3.70574 −0.253319
\(215\) −6.32258 −0.431196
\(216\) −19.9197 −1.35537
\(217\) 0.197046 0.0133764
\(218\) −32.2497 −2.18422
\(219\) 3.39031 0.229096
\(220\) −16.6819 −1.12470
\(221\) −3.40616 −0.229123
\(222\) −5.20672 −0.349452
\(223\) −0.113837 −0.00762312 −0.00381156 0.999993i \(-0.501213\pi\)
−0.00381156 + 0.999993i \(0.501213\pi\)
\(224\) 0.150315 0.0100434
\(225\) −2.28662 −0.152441
\(226\) −31.6526 −2.10550
\(227\) −13.7564 −0.913042 −0.456521 0.889713i \(-0.650905\pi\)
−0.456521 + 0.889713i \(0.650905\pi\)
\(228\) 10.3231 0.683667
\(229\) 26.0780 1.72328 0.861640 0.507520i \(-0.169438\pi\)
0.861640 + 0.507520i \(0.169438\pi\)
\(230\) 8.20998 0.541350
\(231\) 0.382751 0.0251831
\(232\) −15.5522 −1.02105
\(233\) 22.1695 1.45237 0.726186 0.687499i \(-0.241291\pi\)
0.726186 + 0.687499i \(0.241291\pi\)
\(234\) 9.19258 0.600938
\(235\) 10.7097 0.698624
\(236\) 50.3375 3.27669
\(237\) −10.5475 −0.685133
\(238\) 0.517308 0.0335321
\(239\) −19.3646 −1.25259 −0.626296 0.779586i \(-0.715430\pi\)
−0.626296 + 0.779586i \(0.715430\pi\)
\(240\) −2.61426 −0.168750
\(241\) −4.97732 −0.320617 −0.160309 0.987067i \(-0.551249\pi\)
−0.160309 + 0.987067i \(0.551249\pi\)
\(242\) −18.9099 −1.21557
\(243\) −16.0041 −1.02667
\(244\) −32.2276 −2.06316
\(245\) −6.98909 −0.446517
\(246\) 3.70375 0.236142
\(247\) −5.28537 −0.336300
\(248\) −8.41559 −0.534390
\(249\) 1.89106 0.119841
\(250\) −2.41769 −0.152908
\(251\) −9.57536 −0.604391 −0.302196 0.953246i \(-0.597720\pi\)
−0.302196 + 0.953246i \(0.597720\pi\)
\(252\) −0.918421 −0.0578551
\(253\) 14.7322 0.926208
\(254\) 48.3065 3.03102
\(255\) 1.73014 0.108346
\(256\) −30.2231 −1.88894
\(257\) −0.881268 −0.0549720 −0.0274860 0.999622i \(-0.508750\pi\)
−0.0274860 + 0.999622i \(0.508750\pi\)
\(258\) −12.9109 −0.803795
\(259\) −0.266337 −0.0165494
\(260\) 6.39386 0.396530
\(261\) −7.97153 −0.493425
\(262\) −39.8420 −2.46145
\(263\) −6.00564 −0.370324 −0.185162 0.982708i \(-0.559281\pi\)
−0.185162 + 0.982708i \(0.559281\pi\)
\(264\) −16.3468 −1.00608
\(265\) −11.1272 −0.683539
\(266\) 0.802712 0.0492174
\(267\) 13.1575 0.805226
\(268\) −52.4117 −3.20155
\(269\) 15.3180 0.933956 0.466978 0.884269i \(-0.345343\pi\)
0.466978 + 0.884269i \(0.345343\pi\)
\(270\) −10.7954 −0.656987
\(271\) 28.8293 1.75125 0.875627 0.482987i \(-0.160448\pi\)
0.875627 + 0.482987i \(0.160448\pi\)
\(272\) −6.34029 −0.384437
\(273\) −0.146701 −0.00887874
\(274\) −30.4258 −1.83809
\(275\) −4.33837 −0.261614
\(276\) 11.0287 0.663847
\(277\) 15.1871 0.912507 0.456253 0.889850i \(-0.349191\pi\)
0.456253 + 0.889850i \(0.349191\pi\)
\(278\) 35.8173 2.14818
\(279\) −4.31354 −0.258245
\(280\) −0.465986 −0.0278480
\(281\) 21.8786 1.30517 0.652584 0.757716i \(-0.273685\pi\)
0.652584 + 0.757716i \(0.273685\pi\)
\(282\) 21.8695 1.30231
\(283\) −16.0809 −0.955908 −0.477954 0.878385i \(-0.658621\pi\)
−0.477954 + 0.878385i \(0.658621\pi\)
\(284\) −2.00454 −0.118947
\(285\) 2.68468 0.159027
\(286\) 17.4410 1.03131
\(287\) 0.189456 0.0111832
\(288\) −3.29055 −0.193897
\(289\) −12.8039 −0.753173
\(290\) −8.42845 −0.494936
\(291\) 13.7404 0.805475
\(292\) −15.4347 −0.903248
\(293\) 14.0914 0.823227 0.411613 0.911359i \(-0.364965\pi\)
0.411613 + 0.911359i \(0.364965\pi\)
\(294\) −14.2719 −0.832353
\(295\) 13.0910 0.762186
\(296\) 11.3749 0.661153
\(297\) −19.3716 −1.12405
\(298\) −28.2789 −1.63815
\(299\) −5.64658 −0.326550
\(300\) −3.24773 −0.187508
\(301\) −0.660423 −0.0380662
\(302\) 8.06871 0.464302
\(303\) 6.64766 0.381898
\(304\) −9.83829 −0.564265
\(305\) −8.38124 −0.479909
\(306\) −11.3244 −0.647372
\(307\) −17.2957 −0.987117 −0.493559 0.869713i \(-0.664304\pi\)
−0.493559 + 0.869713i \(0.664304\pi\)
\(308\) −1.74251 −0.0992886
\(309\) 8.64361 0.491718
\(310\) −4.56079 −0.259035
\(311\) 4.52172 0.256403 0.128202 0.991748i \(-0.459080\pi\)
0.128202 + 0.991748i \(0.459080\pi\)
\(312\) 6.26541 0.354709
\(313\) 29.9128 1.69077 0.845386 0.534155i \(-0.179370\pi\)
0.845386 + 0.534155i \(0.179370\pi\)
\(314\) 8.20803 0.463206
\(315\) −0.238848 −0.0134576
\(316\) 48.0184 2.70125
\(317\) 10.6496 0.598139 0.299069 0.954231i \(-0.403324\pi\)
0.299069 + 0.954231i \(0.403324\pi\)
\(318\) −22.7220 −1.27419
\(319\) −15.1243 −0.846797
\(320\) −9.66955 −0.540544
\(321\) −1.29460 −0.0722575
\(322\) 0.857571 0.0477906
\(323\) 6.51108 0.362286
\(324\) 11.8758 0.659769
\(325\) 1.66281 0.0922363
\(326\) −10.6765 −0.591319
\(327\) −11.2664 −0.623035
\(328\) −8.09142 −0.446774
\(329\) 1.11868 0.0616748
\(330\) −8.85906 −0.487675
\(331\) 14.3950 0.791219 0.395610 0.918419i \(-0.370533\pi\)
0.395610 + 0.918419i \(0.370533\pi\)
\(332\) −8.60921 −0.472492
\(333\) 5.83038 0.319503
\(334\) 28.3249 1.54987
\(335\) −13.6304 −0.744708
\(336\) −0.273072 −0.0148973
\(337\) −30.9679 −1.68693 −0.843464 0.537186i \(-0.819487\pi\)
−0.843464 + 0.537186i \(0.819487\pi\)
\(338\) 24.7451 1.34596
\(339\) −11.0578 −0.600579
\(340\) −7.87663 −0.427170
\(341\) −8.18402 −0.443189
\(342\) −17.5722 −0.950194
\(343\) −1.46123 −0.0788989
\(344\) 28.2058 1.52076
\(345\) 2.86816 0.154416
\(346\) 25.2838 1.35926
\(347\) −12.7815 −0.686146 −0.343073 0.939309i \(-0.611468\pi\)
−0.343073 + 0.939309i \(0.611468\pi\)
\(348\) −11.3221 −0.606930
\(349\) 4.64674 0.248734 0.124367 0.992236i \(-0.460310\pi\)
0.124367 + 0.992236i \(0.460310\pi\)
\(350\) −0.252539 −0.0134988
\(351\) 7.42476 0.396304
\(352\) −6.24311 −0.332759
\(353\) −4.85486 −0.258398 −0.129199 0.991619i \(-0.541241\pi\)
−0.129199 + 0.991619i \(0.541241\pi\)
\(354\) 26.7321 1.42079
\(355\) −0.521308 −0.0276681
\(356\) −59.9008 −3.17473
\(357\) 0.180722 0.00956481
\(358\) −12.2173 −0.645706
\(359\) −29.4161 −1.55252 −0.776262 0.630410i \(-0.782887\pi\)
−0.776262 + 0.630410i \(0.782887\pi\)
\(360\) 10.2009 0.537635
\(361\) −8.89670 −0.468247
\(362\) −29.0751 −1.52815
\(363\) −6.60617 −0.346734
\(364\) 0.667869 0.0350059
\(365\) −4.01401 −0.210103
\(366\) −17.1147 −0.894600
\(367\) −4.40442 −0.229909 −0.114954 0.993371i \(-0.536672\pi\)
−0.114954 + 0.993371i \(0.536672\pi\)
\(368\) −10.5107 −0.547906
\(369\) −4.14738 −0.215904
\(370\) 6.16457 0.320481
\(371\) −1.16229 −0.0603431
\(372\) −6.12661 −0.317650
\(373\) 14.9927 0.776294 0.388147 0.921597i \(-0.373115\pi\)
0.388147 + 0.921597i \(0.373115\pi\)
\(374\) −21.4856 −1.11099
\(375\) −0.844619 −0.0436159
\(376\) −47.7773 −2.46393
\(377\) 5.79684 0.298553
\(378\) −1.12763 −0.0579991
\(379\) 6.69151 0.343720 0.171860 0.985121i \(-0.445022\pi\)
0.171860 + 0.985121i \(0.445022\pi\)
\(380\) −12.2223 −0.626988
\(381\) 16.8759 0.864579
\(382\) −24.7141 −1.26448
\(383\) −9.14533 −0.467305 −0.233652 0.972320i \(-0.575068\pi\)
−0.233652 + 0.972320i \(0.575068\pi\)
\(384\) −17.3146 −0.883580
\(385\) −0.453164 −0.0230954
\(386\) −9.49396 −0.483230
\(387\) 14.4573 0.734907
\(388\) −62.5543 −3.17571
\(389\) −0.947406 −0.0480354 −0.0240177 0.999712i \(-0.507646\pi\)
−0.0240177 + 0.999712i \(0.507646\pi\)
\(390\) 3.39551 0.171938
\(391\) 6.95606 0.351783
\(392\) 31.1792 1.57479
\(393\) −13.9188 −0.702111
\(394\) 2.02715 0.102126
\(395\) 12.4879 0.628333
\(396\) 38.1452 1.91687
\(397\) 19.6565 0.986530 0.493265 0.869879i \(-0.335803\pi\)
0.493265 + 0.869879i \(0.335803\pi\)
\(398\) −53.8846 −2.70099
\(399\) 0.280428 0.0140389
\(400\) 3.09520 0.154760
\(401\) −5.35715 −0.267523 −0.133762 0.991014i \(-0.542706\pi\)
−0.133762 + 0.991014i \(0.542706\pi\)
\(402\) −27.8336 −1.38821
\(403\) 3.13678 0.156254
\(404\) −30.2641 −1.50569
\(405\) 3.08848 0.153468
\(406\) −0.880392 −0.0436931
\(407\) 11.0619 0.548318
\(408\) −7.71839 −0.382117
\(409\) 1.96328 0.0970781 0.0485390 0.998821i \(-0.484543\pi\)
0.0485390 + 0.998821i \(0.484543\pi\)
\(410\) −4.38511 −0.216565
\(411\) −10.6292 −0.524302
\(412\) −39.3508 −1.93868
\(413\) 1.36741 0.0672860
\(414\) −18.7731 −0.922647
\(415\) −2.23895 −0.109906
\(416\) 2.39286 0.117320
\(417\) 12.5128 0.612753
\(418\) −33.3394 −1.63069
\(419\) −19.4882 −0.952062 −0.476031 0.879428i \(-0.657925\pi\)
−0.476031 + 0.879428i \(0.657925\pi\)
\(420\) −0.339241 −0.0165533
\(421\) 29.4640 1.43599 0.717993 0.696050i \(-0.245061\pi\)
0.717993 + 0.696050i \(0.245061\pi\)
\(422\) 37.1565 1.80875
\(423\) −24.4890 −1.19070
\(424\) 49.6399 2.41073
\(425\) −2.04843 −0.0993634
\(426\) −1.06452 −0.0515763
\(427\) −0.875461 −0.0423665
\(428\) 5.89379 0.284887
\(429\) 6.09300 0.294173
\(430\) 15.2860 0.737157
\(431\) 29.9583 1.44304 0.721521 0.692393i \(-0.243443\pi\)
0.721521 + 0.692393i \(0.243443\pi\)
\(432\) 13.8206 0.664944
\(433\) −33.0683 −1.58916 −0.794581 0.607158i \(-0.792309\pi\)
−0.794581 + 0.607158i \(0.792309\pi\)
\(434\) −0.476396 −0.0228677
\(435\) −2.94448 −0.141177
\(436\) 51.2914 2.45641
\(437\) 10.7938 0.516337
\(438\) −8.19671 −0.391654
\(439\) 7.52782 0.359283 0.179642 0.983732i \(-0.442506\pi\)
0.179642 + 0.983732i \(0.442506\pi\)
\(440\) 19.3540 0.922667
\(441\) 15.9814 0.761018
\(442\) 8.23502 0.391700
\(443\) 8.00794 0.380469 0.190234 0.981739i \(-0.439075\pi\)
0.190234 + 0.981739i \(0.439075\pi\)
\(444\) 8.28101 0.393000
\(445\) −15.5780 −0.738470
\(446\) 0.275223 0.0130322
\(447\) −9.87924 −0.467272
\(448\) −1.01003 −0.0477195
\(449\) −2.17867 −0.102818 −0.0514088 0.998678i \(-0.516371\pi\)
−0.0514088 + 0.998678i \(0.516371\pi\)
\(450\) 5.52833 0.260608
\(451\) −7.86877 −0.370526
\(452\) 50.3418 2.36788
\(453\) 2.81880 0.132439
\(454\) 33.2586 1.56090
\(455\) 0.173689 0.00814266
\(456\) −11.9767 −0.560860
\(457\) 32.2904 1.51048 0.755241 0.655447i \(-0.227520\pi\)
0.755241 + 0.655447i \(0.227520\pi\)
\(458\) −63.0483 −2.94605
\(459\) −9.14661 −0.426927
\(460\) −13.0575 −0.608811
\(461\) −23.4545 −1.09239 −0.546193 0.837659i \(-0.683924\pi\)
−0.546193 + 0.837659i \(0.683924\pi\)
\(462\) −0.925371 −0.0430522
\(463\) −28.8247 −1.33960 −0.669798 0.742543i \(-0.733619\pi\)
−0.669798 + 0.742543i \(0.733619\pi\)
\(464\) 10.7904 0.500930
\(465\) −1.59331 −0.0738880
\(466\) −53.5989 −2.48292
\(467\) −1.68316 −0.0778872 −0.0389436 0.999241i \(-0.512399\pi\)
−0.0389436 + 0.999241i \(0.512399\pi\)
\(468\) −14.6203 −0.675825
\(469\) −1.42376 −0.0657431
\(470\) −25.8927 −1.19434
\(471\) 2.86748 0.132126
\(472\) −58.4005 −2.68810
\(473\) 27.4297 1.26122
\(474\) 25.5005 1.17128
\(475\) −3.17857 −0.145843
\(476\) −0.822752 −0.0377108
\(477\) 25.4437 1.16499
\(478\) 46.8175 2.14138
\(479\) −31.2436 −1.42756 −0.713779 0.700371i \(-0.753018\pi\)
−0.713779 + 0.700371i \(0.753018\pi\)
\(480\) −1.21545 −0.0554772
\(481\) −4.23981 −0.193319
\(482\) 12.0336 0.548115
\(483\) 0.299593 0.0136319
\(484\) 30.0752 1.36705
\(485\) −16.2681 −0.738698
\(486\) 38.6930 1.75515
\(487\) −40.2455 −1.82370 −0.911850 0.410524i \(-0.865346\pi\)
−0.911850 + 0.410524i \(0.865346\pi\)
\(488\) 37.3898 1.69256
\(489\) −3.72985 −0.168670
\(490\) 16.8974 0.763348
\(491\) −29.1839 −1.31705 −0.658526 0.752558i \(-0.728820\pi\)
−0.658526 + 0.752558i \(0.728820\pi\)
\(492\) −5.89062 −0.265570
\(493\) −7.14116 −0.321622
\(494\) 12.7784 0.574926
\(495\) 9.92020 0.445880
\(496\) 5.83886 0.262172
\(497\) −0.0544531 −0.00244255
\(498\) −4.57198 −0.204875
\(499\) −8.91261 −0.398983 −0.199492 0.979900i \(-0.563929\pi\)
−0.199492 + 0.979900i \(0.563929\pi\)
\(500\) 3.84521 0.171963
\(501\) 9.89532 0.442090
\(502\) 23.1502 1.03324
\(503\) 13.6653 0.609304 0.304652 0.952464i \(-0.401460\pi\)
0.304652 + 0.952464i \(0.401460\pi\)
\(504\) 1.06553 0.0474626
\(505\) −7.87060 −0.350237
\(506\) −35.6179 −1.58341
\(507\) 8.64472 0.383925
\(508\) −76.8291 −3.40874
\(509\) 40.6650 1.80244 0.901222 0.433358i \(-0.142671\pi\)
0.901222 + 0.433358i \(0.142671\pi\)
\(510\) −4.18294 −0.185224
\(511\) −0.419283 −0.0185480
\(512\) 32.0703 1.41732
\(513\) −14.1929 −0.626631
\(514\) 2.13063 0.0939780
\(515\) −10.2337 −0.450952
\(516\) 20.5340 0.903961
\(517\) −46.4627 −2.04343
\(518\) 0.643919 0.0282922
\(519\) 8.83290 0.387721
\(520\) −7.41803 −0.325302
\(521\) 13.0700 0.572607 0.286304 0.958139i \(-0.407573\pi\)
0.286304 + 0.958139i \(0.407573\pi\)
\(522\) 19.2727 0.843541
\(523\) 29.4948 1.28972 0.644859 0.764302i \(-0.276916\pi\)
0.644859 + 0.764302i \(0.276916\pi\)
\(524\) 63.3666 2.76818
\(525\) −0.0882245 −0.00385043
\(526\) 14.5198 0.633091
\(527\) −3.86421 −0.168328
\(528\) 11.3416 0.493581
\(529\) −11.4685 −0.498632
\(530\) 26.9021 1.16855
\(531\) −29.9340 −1.29903
\(532\) −1.27667 −0.0553508
\(533\) 3.01595 0.130635
\(534\) −31.8107 −1.37658
\(535\) 1.53276 0.0662671
\(536\) 60.8070 2.62646
\(537\) −4.26813 −0.184183
\(538\) −37.0341 −1.59666
\(539\) 30.3213 1.30603
\(540\) 17.1695 0.738859
\(541\) −5.31616 −0.228560 −0.114280 0.993449i \(-0.536456\pi\)
−0.114280 + 0.993449i \(0.536456\pi\)
\(542\) −69.7002 −2.99388
\(543\) −10.1574 −0.435895
\(544\) −2.94778 −0.126385
\(545\) 13.3391 0.571383
\(546\) 0.354677 0.0151788
\(547\) −16.8087 −0.718689 −0.359345 0.933205i \(-0.617000\pi\)
−0.359345 + 0.933205i \(0.617000\pi\)
\(548\) 48.3906 2.06714
\(549\) 19.1647 0.817930
\(550\) 10.4888 0.447245
\(551\) −11.0810 −0.472067
\(552\) −12.7952 −0.544601
\(553\) 1.30442 0.0554695
\(554\) −36.7177 −1.55999
\(555\) 2.15359 0.0914150
\(556\) −56.9655 −2.41588
\(557\) 24.1887 1.02491 0.512455 0.858714i \(-0.328736\pi\)
0.512455 + 0.858714i \(0.328736\pi\)
\(558\) 10.4288 0.441485
\(559\) −10.5133 −0.444664
\(560\) 0.323308 0.0136623
\(561\) −7.50600 −0.316904
\(562\) −52.8956 −2.23127
\(563\) −9.81018 −0.413450 −0.206725 0.978399i \(-0.566280\pi\)
−0.206725 + 0.978399i \(0.566280\pi\)
\(564\) −34.7823 −1.46460
\(565\) 13.0921 0.550788
\(566\) 38.8785 1.63418
\(567\) 0.322606 0.0135482
\(568\) 2.32562 0.0975809
\(569\) 28.1377 1.17959 0.589797 0.807552i \(-0.299208\pi\)
0.589797 + 0.807552i \(0.299208\pi\)
\(570\) −6.49071 −0.271866
\(571\) 31.0041 1.29748 0.648741 0.761009i \(-0.275296\pi\)
0.648741 + 0.761009i \(0.275296\pi\)
\(572\) −27.7390 −1.15982
\(573\) −8.63387 −0.360685
\(574\) −0.458045 −0.0191184
\(575\) −3.39580 −0.141615
\(576\) 22.1106 0.921274
\(577\) 26.0634 1.08503 0.542516 0.840045i \(-0.317472\pi\)
0.542516 + 0.840045i \(0.317472\pi\)
\(578\) 30.9559 1.28760
\(579\) −3.31672 −0.137838
\(580\) 13.4050 0.556613
\(581\) −0.233869 −0.00970250
\(582\) −33.2199 −1.37701
\(583\) 48.2740 1.99930
\(584\) 17.9070 0.740998
\(585\) −3.80222 −0.157202
\(586\) −34.0685 −1.40736
\(587\) 17.6837 0.729886 0.364943 0.931030i \(-0.381088\pi\)
0.364943 + 0.931030i \(0.381088\pi\)
\(588\) 22.6987 0.936079
\(589\) −5.99613 −0.247066
\(590\) −31.6498 −1.30300
\(591\) 0.708185 0.0291308
\(592\) −7.89207 −0.324362
\(593\) 24.9555 1.02480 0.512400 0.858747i \(-0.328756\pi\)
0.512400 + 0.858747i \(0.328756\pi\)
\(594\) 46.8345 1.92164
\(595\) −0.213968 −0.00877184
\(596\) 44.9762 1.84230
\(597\) −18.8246 −0.770440
\(598\) 13.6517 0.558258
\(599\) 3.49052 0.142619 0.0713093 0.997454i \(-0.477282\pi\)
0.0713093 + 0.997454i \(0.477282\pi\)
\(600\) 3.76795 0.153826
\(601\) 28.5329 1.16388 0.581941 0.813231i \(-0.302294\pi\)
0.581941 + 0.813231i \(0.302294\pi\)
\(602\) 1.59670 0.0650765
\(603\) 31.1675 1.26924
\(604\) −12.8329 −0.522162
\(605\) 7.82147 0.317988
\(606\) −16.0720 −0.652879
\(607\) −29.7118 −1.20597 −0.602983 0.797754i \(-0.706021\pi\)
−0.602983 + 0.797754i \(0.706021\pi\)
\(608\) −4.57411 −0.185504
\(609\) −0.307565 −0.0124632
\(610\) 20.2632 0.820433
\(611\) 17.8082 0.720444
\(612\) 18.0109 0.728046
\(613\) 30.9697 1.25085 0.625426 0.780283i \(-0.284925\pi\)
0.625426 + 0.780283i \(0.284925\pi\)
\(614\) 41.8155 1.68754
\(615\) −1.53194 −0.0617737
\(616\) 2.02162 0.0814534
\(617\) 39.1508 1.57615 0.788077 0.615577i \(-0.211077\pi\)
0.788077 + 0.615577i \(0.211077\pi\)
\(618\) −20.8975 −0.840622
\(619\) 1.32237 0.0531507 0.0265754 0.999647i \(-0.491540\pi\)
0.0265754 + 0.999647i \(0.491540\pi\)
\(620\) 7.25370 0.291315
\(621\) −15.1629 −0.608464
\(622\) −10.9321 −0.438338
\(623\) −1.62720 −0.0651924
\(624\) −4.34703 −0.174020
\(625\) 1.00000 0.0400000
\(626\) −72.3198 −2.89048
\(627\) −11.6471 −0.465142
\(628\) −13.0544 −0.520929
\(629\) 5.22305 0.208257
\(630\) 0.577460 0.0230066
\(631\) −15.0516 −0.599193 −0.299596 0.954066i \(-0.596852\pi\)
−0.299596 + 0.954066i \(0.596852\pi\)
\(632\) −55.7100 −2.21602
\(633\) 12.9806 0.515934
\(634\) −25.7473 −1.02256
\(635\) −19.9805 −0.792901
\(636\) 36.1382 1.43297
\(637\) −11.6216 −0.460463
\(638\) 36.5658 1.44765
\(639\) 1.19203 0.0471561
\(640\) 20.4998 0.810328
\(641\) 32.6162 1.28826 0.644131 0.764915i \(-0.277219\pi\)
0.644131 + 0.764915i \(0.277219\pi\)
\(642\) 3.12994 0.123529
\(643\) 24.9480 0.983851 0.491926 0.870637i \(-0.336293\pi\)
0.491926 + 0.870637i \(0.336293\pi\)
\(644\) −1.36392 −0.0537461
\(645\) 5.34017 0.210269
\(646\) −15.7417 −0.619350
\(647\) 1.93744 0.0761688 0.0380844 0.999275i \(-0.487874\pi\)
0.0380844 + 0.999275i \(0.487874\pi\)
\(648\) −13.7781 −0.541255
\(649\) −56.7935 −2.22934
\(650\) −4.02016 −0.157684
\(651\) −0.166429 −0.00652287
\(652\) 16.9805 0.665007
\(653\) −22.3056 −0.872886 −0.436443 0.899732i \(-0.643762\pi\)
−0.436443 + 0.899732i \(0.643762\pi\)
\(654\) 27.2387 1.06512
\(655\) 16.4794 0.643903
\(656\) 5.61395 0.219188
\(657\) 9.17851 0.358088
\(658\) −2.70462 −0.105437
\(659\) −9.73679 −0.379291 −0.189646 0.981853i \(-0.560734\pi\)
−0.189646 + 0.981853i \(0.560734\pi\)
\(660\) 14.0899 0.548448
\(661\) −45.3185 −1.76268 −0.881342 0.472479i \(-0.843359\pi\)
−0.881342 + 0.472479i \(0.843359\pi\)
\(662\) −34.8025 −1.35264
\(663\) 2.87691 0.111730
\(664\) 9.98822 0.387618
\(665\) −0.332017 −0.0128751
\(666\) −14.0960 −0.546210
\(667\) −11.8383 −0.458382
\(668\) −45.0493 −1.74301
\(669\) 0.0961493 0.00371735
\(670\) 32.9540 1.27313
\(671\) 36.3609 1.40370
\(672\) −0.126959 −0.00489755
\(673\) 24.7710 0.954851 0.477425 0.878672i \(-0.341570\pi\)
0.477425 + 0.878672i \(0.341570\pi\)
\(674\) 74.8706 2.88391
\(675\) 4.46518 0.171865
\(676\) −39.3559 −1.51369
\(677\) −20.6154 −0.792314 −0.396157 0.918183i \(-0.629656\pi\)
−0.396157 + 0.918183i \(0.629656\pi\)
\(678\) 26.7344 1.02673
\(679\) −1.69928 −0.0652125
\(680\) 9.13831 0.350438
\(681\) 11.6189 0.445237
\(682\) 19.7864 0.757660
\(683\) 0.616035 0.0235719 0.0117860 0.999931i \(-0.496248\pi\)
0.0117860 + 0.999931i \(0.496248\pi\)
\(684\) 27.9476 1.06860
\(685\) 12.5847 0.480835
\(686\) 3.53279 0.134882
\(687\) −22.0259 −0.840342
\(688\) −19.5696 −0.746084
\(689\) −18.5025 −0.704888
\(690\) −6.93430 −0.263984
\(691\) 17.8270 0.678173 0.339086 0.940755i \(-0.389882\pi\)
0.339086 + 0.940755i \(0.389882\pi\)
\(692\) −40.2126 −1.52865
\(693\) 1.03621 0.0393625
\(694\) 30.9016 1.17301
\(695\) −14.8147 −0.561953
\(696\) 13.1357 0.497908
\(697\) −3.71536 −0.140729
\(698\) −11.2343 −0.425226
\(699\) −18.7248 −0.708236
\(700\) 0.401650 0.0151809
\(701\) 18.7168 0.706922 0.353461 0.935449i \(-0.385005\pi\)
0.353461 + 0.935449i \(0.385005\pi\)
\(702\) −17.9507 −0.677507
\(703\) 8.10466 0.305673
\(704\) 41.9501 1.58105
\(705\) −9.04562 −0.340678
\(706\) 11.7375 0.441748
\(707\) −0.822122 −0.0309191
\(708\) −42.5160 −1.59785
\(709\) 22.1260 0.830961 0.415481 0.909602i \(-0.363613\pi\)
0.415481 + 0.909602i \(0.363613\pi\)
\(710\) 1.26036 0.0473004
\(711\) −28.5550 −1.07090
\(712\) 69.4956 2.60446
\(713\) −6.40592 −0.239904
\(714\) −0.436928 −0.0163516
\(715\) −7.21391 −0.269785
\(716\) 19.4310 0.726172
\(717\) 16.3557 0.610815
\(718\) 71.1190 2.65414
\(719\) 23.8375 0.888987 0.444493 0.895782i \(-0.353384\pi\)
0.444493 + 0.895782i \(0.353384\pi\)
\(720\) −7.07753 −0.263764
\(721\) −1.06896 −0.0398102
\(722\) 21.5094 0.800498
\(723\) 4.20394 0.156346
\(724\) 46.2424 1.71859
\(725\) 3.48617 0.129473
\(726\) 15.9716 0.592763
\(727\) 35.9199 1.33220 0.666098 0.745864i \(-0.267963\pi\)
0.666098 + 0.745864i \(0.267963\pi\)
\(728\) −0.774848 −0.0287178
\(729\) 4.25195 0.157480
\(730\) 9.70462 0.359184
\(731\) 12.9514 0.479023
\(732\) 27.2200 1.00608
\(733\) 49.6436 1.83363 0.916813 0.399316i \(-0.130752\pi\)
0.916813 + 0.399316i \(0.130752\pi\)
\(734\) 10.6485 0.393043
\(735\) 5.90312 0.217740
\(736\) −4.88671 −0.180127
\(737\) 59.1337 2.17822
\(738\) 10.0271 0.369101
\(739\) −5.97744 −0.219884 −0.109942 0.993938i \(-0.535066\pi\)
−0.109942 + 0.993938i \(0.535066\pi\)
\(740\) −9.80444 −0.360418
\(741\) 4.46412 0.163994
\(742\) 2.81005 0.103160
\(743\) −17.2264 −0.631977 −0.315988 0.948763i \(-0.602336\pi\)
−0.315988 + 0.948763i \(0.602336\pi\)
\(744\) 7.10797 0.260591
\(745\) 11.6967 0.428533
\(746\) −36.2477 −1.32712
\(747\) 5.11962 0.187317
\(748\) 34.1718 1.24944
\(749\) 0.160104 0.00585008
\(750\) 2.04202 0.0745642
\(751\) 46.3306 1.69063 0.845313 0.534272i \(-0.179414\pi\)
0.845313 + 0.534272i \(0.179414\pi\)
\(752\) 33.1486 1.20881
\(753\) 8.08753 0.294726
\(754\) −14.0149 −0.510394
\(755\) −3.33737 −0.121459
\(756\) 1.79344 0.0652268
\(757\) −35.9850 −1.30790 −0.653949 0.756538i \(-0.726889\pi\)
−0.653949 + 0.756538i \(0.726889\pi\)
\(758\) −16.1780 −0.587611
\(759\) −12.4431 −0.451657
\(760\) 14.1800 0.514363
\(761\) 50.2019 1.81982 0.909908 0.414810i \(-0.136152\pi\)
0.909908 + 0.414810i \(0.136152\pi\)
\(762\) −40.8006 −1.47805
\(763\) 1.39333 0.0504419
\(764\) 39.3065 1.42206
\(765\) 4.68398 0.169350
\(766\) 22.1105 0.798886
\(767\) 21.7678 0.785991
\(768\) 25.5270 0.921126
\(769\) 34.4616 1.24272 0.621358 0.783527i \(-0.286581\pi\)
0.621358 + 0.783527i \(0.286581\pi\)
\(770\) 1.09561 0.0394830
\(771\) 0.744336 0.0268066
\(772\) 15.0997 0.543449
\(773\) 34.1443 1.22808 0.614042 0.789274i \(-0.289543\pi\)
0.614042 + 0.789274i \(0.289543\pi\)
\(774\) −34.9533 −1.25637
\(775\) 1.88643 0.0677624
\(776\) 72.5742 2.60526
\(777\) 0.224953 0.00807015
\(778\) 2.29053 0.0821195
\(779\) −5.76517 −0.206559
\(780\) −5.40038 −0.193365
\(781\) 2.26163 0.0809274
\(782\) −16.8176 −0.601395
\(783\) 15.5664 0.556296
\(784\) −21.6326 −0.772593
\(785\) −3.39499 −0.121173
\(786\) 33.6513 1.20030
\(787\) 49.1699 1.75272 0.876359 0.481659i \(-0.159965\pi\)
0.876359 + 0.481659i \(0.159965\pi\)
\(788\) −3.22407 −0.114853
\(789\) 5.07248 0.180585
\(790\) −30.1917 −1.07417
\(791\) 1.36753 0.0486238
\(792\) −44.2553 −1.57254
\(793\) −13.9364 −0.494898
\(794\) −47.5232 −1.68654
\(795\) 9.39825 0.333322
\(796\) 85.7007 3.03758
\(797\) −1.19443 −0.0423089 −0.0211544 0.999776i \(-0.506734\pi\)
−0.0211544 + 0.999776i \(0.506734\pi\)
\(798\) −0.677986 −0.0240004
\(799\) −21.9381 −0.776113
\(800\) 1.43905 0.0508779
\(801\) 35.6210 1.25861
\(802\) 12.9519 0.457348
\(803\) 17.4143 0.614537
\(804\) 44.2679 1.56121
\(805\) −0.354707 −0.0125018
\(806\) −7.58374 −0.267126
\(807\) −12.9379 −0.455435
\(808\) 35.1118 1.23523
\(809\) 26.1186 0.918281 0.459141 0.888364i \(-0.348157\pi\)
0.459141 + 0.888364i \(0.348157\pi\)
\(810\) −7.46697 −0.262363
\(811\) 21.4096 0.751794 0.375897 0.926661i \(-0.377335\pi\)
0.375897 + 0.926661i \(0.377335\pi\)
\(812\) 1.40022 0.0491380
\(813\) −24.3498 −0.853984
\(814\) −26.7442 −0.937384
\(815\) 4.41601 0.154686
\(816\) 5.35513 0.187467
\(817\) 20.0967 0.703096
\(818\) −4.74660 −0.165961
\(819\) −0.397160 −0.0138779
\(820\) 6.97429 0.243553
\(821\) −40.4726 −1.41250 −0.706252 0.707960i \(-0.749616\pi\)
−0.706252 + 0.707960i \(0.749616\pi\)
\(822\) 25.6982 0.896327
\(823\) −26.8616 −0.936335 −0.468168 0.883640i \(-0.655086\pi\)
−0.468168 + 0.883640i \(0.655086\pi\)
\(824\) 45.6540 1.59043
\(825\) 3.66427 0.127574
\(826\) −3.30598 −0.115030
\(827\) −9.44610 −0.328473 −0.164237 0.986421i \(-0.552516\pi\)
−0.164237 + 0.986421i \(0.552516\pi\)
\(828\) 29.8576 1.03762
\(829\) 53.9909 1.87518 0.937590 0.347743i \(-0.113052\pi\)
0.937590 + 0.347743i \(0.113052\pi\)
\(830\) 5.41307 0.187890
\(831\) −12.8274 −0.444976
\(832\) −16.0787 −0.557427
\(833\) 14.3167 0.496043
\(834\) −30.2520 −1.04754
\(835\) −11.7157 −0.405439
\(836\) 53.0247 1.83390
\(837\) 8.42323 0.291149
\(838\) 47.1164 1.62761
\(839\) 0.817512 0.0282237 0.0141118 0.999900i \(-0.495508\pi\)
0.0141118 + 0.999900i \(0.495508\pi\)
\(840\) 0.393581 0.0135798
\(841\) −16.8467 −0.580919
\(842\) −71.2347 −2.45491
\(843\) −18.4791 −0.636454
\(844\) −59.0955 −2.03415
\(845\) −10.2350 −0.352096
\(846\) 59.2067 2.03557
\(847\) 0.816990 0.0280721
\(848\) −34.4409 −1.18270
\(849\) 13.5822 0.466140
\(850\) 4.95246 0.169868
\(851\) 8.65855 0.296811
\(852\) 1.69307 0.0580036
\(853\) −3.25549 −0.111466 −0.0557330 0.998446i \(-0.517750\pi\)
−0.0557330 + 0.998446i \(0.517750\pi\)
\(854\) 2.11659 0.0724282
\(855\) 7.26817 0.248566
\(856\) −6.83785 −0.233713
\(857\) −6.87376 −0.234803 −0.117402 0.993085i \(-0.537456\pi\)
−0.117402 + 0.993085i \(0.537456\pi\)
\(858\) −14.7310 −0.502907
\(859\) 0.0404079 0.00137870 0.000689349 1.00000i \(-0.499781\pi\)
0.000689349 1.00000i \(0.499781\pi\)
\(860\) −24.3116 −0.829019
\(861\) −0.160018 −0.00545341
\(862\) −72.4298 −2.46697
\(863\) −6.31529 −0.214975 −0.107487 0.994206i \(-0.534281\pi\)
−0.107487 + 0.994206i \(0.534281\pi\)
\(864\) 6.42560 0.218603
\(865\) −10.4578 −0.355577
\(866\) 79.9488 2.71677
\(867\) 10.8144 0.367278
\(868\) 0.757683 0.0257174
\(869\) −54.1770 −1.83783
\(870\) 7.11883 0.241351
\(871\) −22.6648 −0.767968
\(872\) −59.5073 −2.01517
\(873\) 37.1990 1.25900
\(874\) −26.0960 −0.882710
\(875\) 0.104455 0.00353122
\(876\) 13.0364 0.440461
\(877\) −48.9066 −1.65146 −0.825730 0.564066i \(-0.809236\pi\)
−0.825730 + 0.564066i \(0.809236\pi\)
\(878\) −18.1999 −0.614217
\(879\) −11.9018 −0.401439
\(880\) −13.4281 −0.452661
\(881\) −19.0695 −0.642469 −0.321235 0.947000i \(-0.604098\pi\)
−0.321235 + 0.947000i \(0.604098\pi\)
\(882\) −38.6380 −1.30101
\(883\) 35.3490 1.18959 0.594794 0.803878i \(-0.297234\pi\)
0.594794 + 0.803878i \(0.297234\pi\)
\(884\) −13.0974 −0.440512
\(885\) −11.0569 −0.371673
\(886\) −19.3607 −0.650435
\(887\) 34.5067 1.15862 0.579311 0.815107i \(-0.303322\pi\)
0.579311 + 0.815107i \(0.303322\pi\)
\(888\) −9.60746 −0.322405
\(889\) −2.08706 −0.0699976
\(890\) 37.6628 1.26246
\(891\) −13.3990 −0.448883
\(892\) −0.437729 −0.0146562
\(893\) −34.0415 −1.13916
\(894\) 23.8849 0.798831
\(895\) 5.05332 0.168914
\(896\) 2.14131 0.0715360
\(897\) 4.76921 0.159239
\(898\) 5.26733 0.175773
\(899\) 6.57639 0.219335
\(900\) −8.79252 −0.293084
\(901\) 22.7933 0.759355
\(902\) 19.0242 0.633437
\(903\) 0.557806 0.0185626
\(904\) −58.4055 −1.94254
\(905\) 12.0260 0.399757
\(906\) −6.81498 −0.226413
\(907\) 12.5195 0.415703 0.207851 0.978160i \(-0.433353\pi\)
0.207851 + 0.978160i \(0.433353\pi\)
\(908\) −52.8961 −1.75542
\(909\) 17.9971 0.596925
\(910\) −0.419925 −0.0139204
\(911\) −14.5086 −0.480692 −0.240346 0.970687i \(-0.577261\pi\)
−0.240346 + 0.970687i \(0.577261\pi\)
\(912\) 8.30961 0.275159
\(913\) 9.71338 0.321466
\(914\) −78.0681 −2.58226
\(915\) 7.07896 0.234023
\(916\) 100.275 3.31318
\(917\) 1.72135 0.0568440
\(918\) 22.1136 0.729858
\(919\) 43.6588 1.44017 0.720085 0.693885i \(-0.244103\pi\)
0.720085 + 0.693885i \(0.244103\pi\)
\(920\) 15.1491 0.499451
\(921\) 14.6083 0.481359
\(922\) 56.7057 1.86750
\(923\) −0.866838 −0.0285323
\(924\) 1.47176 0.0484172
\(925\) −2.54978 −0.0838363
\(926\) 69.6890 2.29012
\(927\) 23.4007 0.768578
\(928\) 5.01675 0.164683
\(929\) 37.3685 1.22602 0.613010 0.790075i \(-0.289958\pi\)
0.613010 + 0.790075i \(0.289958\pi\)
\(930\) 3.85213 0.126316
\(931\) 22.2153 0.728077
\(932\) 85.2462 2.79233
\(933\) −3.81913 −0.125033
\(934\) 4.06935 0.133153
\(935\) 8.88685 0.290631
\(936\) 16.9622 0.554427
\(937\) −6.91459 −0.225890 −0.112945 0.993601i \(-0.536028\pi\)
−0.112945 + 0.993601i \(0.536028\pi\)
\(938\) 3.44221 0.112392
\(939\) −25.2649 −0.824490
\(940\) 41.1810 1.34318
\(941\) −11.8124 −0.385074 −0.192537 0.981290i \(-0.561672\pi\)
−0.192537 + 0.981290i \(0.561672\pi\)
\(942\) −6.93266 −0.225878
\(943\) −6.15917 −0.200570
\(944\) 40.5191 1.31878
\(945\) 0.466409 0.0151723
\(946\) −66.3164 −2.15613
\(947\) −58.2529 −1.89297 −0.946483 0.322754i \(-0.895391\pi\)
−0.946483 + 0.322754i \(0.895391\pi\)
\(948\) −40.5573 −1.31724
\(949\) −6.67456 −0.216665
\(950\) 7.68478 0.249327
\(951\) −8.99482 −0.291677
\(952\) 0.954540 0.0309368
\(953\) −4.74730 −0.153780 −0.0768900 0.997040i \(-0.524499\pi\)
−0.0768900 + 0.997040i \(0.524499\pi\)
\(954\) −61.5148 −1.99162
\(955\) 10.2222 0.330783
\(956\) −74.4608 −2.40824
\(957\) 12.7743 0.412933
\(958\) 75.5373 2.44050
\(959\) 1.31453 0.0424483
\(960\) 8.16709 0.263592
\(961\) −27.4414 −0.885206
\(962\) 10.2505 0.330491
\(963\) −3.50484 −0.112942
\(964\) −19.1388 −0.616420
\(965\) 3.92688 0.126411
\(966\) −0.724321 −0.0233047
\(967\) 6.34545 0.204056 0.102028 0.994782i \(-0.467467\pi\)
0.102028 + 0.994782i \(0.467467\pi\)
\(968\) −34.8926 −1.12149
\(969\) −5.49938 −0.176666
\(970\) 39.3312 1.26285
\(971\) 49.5490 1.59010 0.795051 0.606542i \(-0.207444\pi\)
0.795051 + 0.606542i \(0.207444\pi\)
\(972\) −61.5392 −1.97387
\(973\) −1.54747 −0.0496095
\(974\) 97.3011 3.11773
\(975\) −1.40444 −0.0449782
\(976\) −25.9416 −0.830370
\(977\) −33.9307 −1.08554 −0.542770 0.839881i \(-0.682625\pi\)
−0.542770 + 0.839881i \(0.682625\pi\)
\(978\) 9.01761 0.288351
\(979\) 67.5833 2.15997
\(980\) −26.8745 −0.858474
\(981\) −30.5013 −0.973833
\(982\) 70.5576 2.25158
\(983\) −52.2834 −1.66758 −0.833791 0.552080i \(-0.813834\pi\)
−0.833791 + 0.552080i \(0.813834\pi\)
\(984\) 6.83417 0.217865
\(985\) −0.838466 −0.0267158
\(986\) 17.2651 0.549833
\(987\) −0.944858 −0.0300752
\(988\) −20.3233 −0.646571
\(989\) 21.4702 0.682713
\(990\) −23.9839 −0.762259
\(991\) −48.3161 −1.53481 −0.767406 0.641162i \(-0.778453\pi\)
−0.767406 + 0.641162i \(0.778453\pi\)
\(992\) 2.71465 0.0861903
\(993\) −12.1583 −0.385831
\(994\) 0.131650 0.00417570
\(995\) 22.2877 0.706567
\(996\) 7.27150 0.230406
\(997\) −39.3971 −1.24772 −0.623860 0.781536i \(-0.714436\pi\)
−0.623860 + 0.781536i \(0.714436\pi\)
\(998\) 21.5479 0.682087
\(999\) −11.3852 −0.360213
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))